In digital imaging, de-convolution is sometimes used to create better images by correcting optical aberrations, such as optical blurring, optical distortion, chromatic aberration, field curvature, etc., that take place in an imaging instrument, such as a digital camera. The mathematical operation that defines de-convolution is the same mathematical operation that is performed in convolution—the reason for naming it de-convolution is that it is used in a context of correcting or compensating for an effect that is applied on the image by convolution. In other words, the use of de-convolution—in this manner—is based on the fact that when an image signal passes through an imaging instrument, it is possible to describe the output signal as a convolution between the image signal and a 2D function called a point spread function (PSF). Using optical blurring as an example, the PSF describes the optical blurring in terms of the pathway a point source of electromagnetic radiation takes through the instrument, i.e., how a single point of light is imaged through the optical system. The result of the PSF convolution is that the captured image signal is more blurred than the object itself (and can also be distorted, and/or contain color aberrations). In order to compensate for this blurring, a de-convolution process can be performed, in which the image signal is convolved with a 2D function that is aimed to produce a non-blurred image. This 2D function is often an inverse of the PSF (or a variation of the inverse of the PSF) in a way that it undoes the blurring the PSF introduces.
A 2D de-convolution can be performed in the digital domain, on a digital representation of an image, in software (SW) or hardware (HW). A kernel matrix is usually used as the 2D de-convolution filter, which can be characterized by a desired frequency response. The kernel matrix is convolved with a signal matrix (the 2D image) in order to compensate for the PSF blur and enhance the contrast in the image. In order for the filter to enhance contrast, it should have a frequency response of a band-pass filter (BPF) or high-pass filter (HPF), such that it matches the PSF in a way that the contrast in required frequencies is enhanced to a specified level.
In addition to enhancing the contrast in the image, the same convolution operation can be used to reduce noise in the image, by applying kernels with low-pass frequency response (LPF) on it, averaging the noise. Care should be taken not to damage the signal's contrast when performing such a de-noising operation.
Usually, the de-convolution process that enhances the image is a part of an image signal processing (ISP) chain that is run in the digital camera (in SW or HW). This chain of mathematical operations on the image transforms it from a “RAW” format image (sometimes referred to as a “NEF” image) that the CMOS/CCD sensor outputs (in e.g., “BAYER” format), to a final image (e.g., a JPEG image, a TIFF image, etc.) that is viewed and saved. Within the ISP chain, applying the de-convolution filters on the image may be done after performing de-mosaicing (color interpolation), or before de-mosaicing. The former method enables the filter to affect the maximum possible frequencies in the image (pixel-by-pixel); however, in order to cover a large spatial support, the 2D kernel should have many coefficients. The latter method implies applying the filter while the image is still in BAYER format (before color interpolation). The latter method has the advantage of covering a larger spatial support for fewer coefficients, but the filters can only affect lower frequencies. Since for most optical designs, the size of the kernel should be about the same as the size of the PSF (in pixels) in order for the de-convolution to be effective, compensating for large PSFs requires large enough spatial support for the de-convolution kernels, and thus many coefficients (which implies more memory and mathematical calculations). This might be a prime reason for applying the de-convolution kernels on the BAYER image before the demosaicing process, because if too small kernels are applied on an image that is blurred by a large PSF, then undesired artifacts may remain after the processing.
While applying a de-convolution filter with a HPF/BPF frequency response on an image might result in increased contrast, it may also undesirably amplify noise. This noise amplification is less noticeable when the signal-to-noise ratio (S/N) is good, and is most noticeable in bad light conditions, which can cause low S/N. Unfortunately, applying de-convolution kernels without regarding the amount of noise already in the image may lead to noisier images.
A denoising algorithm might be applied to reduce the unwanted noise amplification that results from applying de-convolution kernels. However, applying denoising algorithms after the de-convolution process has already amplified the noise in the image could require performing strong de-noising, which may cause unwanted loss of data in areas with fine-details in the image. Moreover, applying strong denoising still will not remove all of the noise.
The approaches described in this section are approaches that could be pursued, but not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section.